Apart from dynamics the pseudo-arc appears also in isometric theory of Banach spaces, as a counterexample [1]}, [2]} to Wood's Conjecture [3]}, which asserted that there exists no non-degenerate almost transitive space. A closely related result was obtained by Irwin and Solecki in a seminal paper [4]}, where using tools from model theory they developed a dualization of the classical Fraïssé limit construction, and obtained surjective universality and projective homogeneity of the pseudo-arc in the class of arc-like continua. This result gave a new characterization of the pseudo-arc and initiated a new research direction. One of the most notable results that followed is the result of Kwiatkowska [5]}, who proved that the automorphisms group of the pseudo-arc has a residual conjugacy class. A difficult open problem that arose in this direction of research asks to describe the universal minimal flow of the homeomorphism group of the pseudo-arc, see e.g. [6]}. This problem is only one of the many present in the literature that aim at improving the understanding of the homeomorphism group of the pseudo-arc. Other open questions include those asking about covering dimension of that group [7]}, or whether it contains the Erdös spaceThis question was raised by Logan Hoehn at Spring Topology and Dynamics Conference in 2019. The Erdös space consists of all vectors in the real Hilbert space \(\ell ^2\)  that have only rational coordinates..
